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Math Help - nilpotent matrices

  1. #1
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    nilpotent matrices

    are all nilpotent matrices singular?
    if so, how is that possible?

    cheers
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  2. #2
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    Quote Originally Posted by the wildcat View Post
    are all nilpotent matrices singular?
    if so, how is that possible?

    cheers
    Yes.

    I quote from Nilpotent matrix - Wikipedia, the free encyclopedia:

    "Over an algebraically closed field, a matrix M is nilpotent if and only if its eigenvalues are all zero. Therefore the determinant and trace of M are both zero, and nilpotent matrices are not invertible."
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